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A general multivariate threshold GARCH model with dynamic conditional correlations

  • Francesco Audrino

    ()

  • Fabio Trojani

    ()

We propose a new multivariate GARCH model with Dynamic Conditional Correlations that extends previous models by admitting multivariate thresholds in conditional volatilities and correlations. The model estimation is feasible in large dimensions and the positive deniteness of the conditional covariance matrix is easily ensured by the structure of the model. Thresholds in conditional volatilities and correlations are estimated from the data, together with all other model parameters. We study the performance of our model in three distinct applications to US stock and bond market data. Even if the conditional volatility functions of stock returns exhibit pronounced GARCH and threshold features, their conditional correlation dynamics depends on a very simple threshold structure with no local GARCH features. We obtain a similar result for the conditional correlations between government and corporate bond returns. On the contrary, we ¯nd both threshold and GARCH structures in the conditional correlations between stock and government bond returns. In all applications, our model improves signi¯cantly the in-sample and out-of-sample forecasting power for future conditional correlations with respect to other relevant multivariate GARCH models.

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Paper provided by Department of Economics, University of St. Gallen in its series University of St. Gallen Department of Economics working paper series 2007 with number 2007-25.

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Length: 34 pages
Date of creation: Apr 2007
Date of revision:
Handle: RePEc:usg:dp2007:2007-25
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  1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  2. Bae, Kee-Hong & Andrew Karolyi, G., 1994. "Good news, bad news and international spillovers of stock return volatility between Japan and the U.S," Pacific-Basin Finance Journal, Elsevier, vol. 2(4), pages 405-438, December.
  3. Ledoit, Olivier & Santa-Clara, Pedro & Wolf, Michael, 1999. "Flexible Multivariate GARCH Modeling With an Application to International Stock Markets," University of California at Los Angeles, Anderson Graduate School of Management qt93s6p8gb, Anderson Graduate School of Management, UCLA.
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  8. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
  9. Fulvio Corsi & Francesco Audrino, 2007. "Realized Correlation Tick-by-Tick," University of St. Gallen Department of Economics working paper series 2007 2007-02, Department of Economics, University of St. Gallen.
  10. Becker, Kent G. & Finnerty, Joseph E. & Friedman, Joseph, 1995. "Economic news and equity market linkages between the U.S. and U.K," Journal of Banking & Finance, Elsevier, vol. 19(7), pages 1191-1210, October.
  11. Fabio Trojani & Francesco Audrino, 2006. "Estimating and predicting multivariate volatility thresholds in global stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 345-369.
  12. Engle, Robert F & Ito, Takatoshi & Lin, Wen-Ling, 1990. "Meteor Showers or Heat Waves? Heteroskedastic Intra-daily Volatility in the Foreign Exchange Market," Econometrica, Econometric Society, vol. 58(3), pages 525-42, May.
  13. Mervyn A. King & Sushil Wadhwani, 1989. "Transmission of Volatility Between Stock Markets," NBER Working Papers 2910, National Bureau of Economic Research, Inc.
  14. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
  15. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  16. Hamao, Yasushi & Masulis, Ronald W & Ng, Victor, 1990. "Correlations in Price Changes and Volatility across International Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 3(2), pages 281-307.
  17. Koutmos, Gregory & Booth, G Geoffrey, 1995. "Asymmetric volatility transmission in international stock markets," Journal of International Money and Finance, Elsevier, vol. 14(6), pages 747-762, December.
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